A/C compressor pulley seized

We thought the alternator was bad because the car did not start and after replacing the battery it worked then stopped again, after getting it a jump and getting it back home, the serpentine belt broke very clean. We checked all pulleys, they spun fine, we replaced the belt, started it up, it made a huge squeak, and this time shredded the belt a little, but it broke also. We then noticed the air compressor pulley did not move at all, it’s winter so A/C has not been running. could there be another issue that would have made that pulley lock up? No free spinning at all.